Complex genetic diseases exhibit greater or lesser degrees of familial aggregation but do not fit simple Medelian patterns of inheritance. Presumably, genes and environment both contribute to the occurrence of these diseases. Since genes act in only a few, well understood ways, it seems logical to identify genetic factors first, then use them to sort out environmental contributions. Gene linkage analysis represents one powerful tool for identifying specific genes, detecting genetic heterogeneity, and predicting recurrence risks. A number of these complex diseases exhibit striking and consistent disease-marker associations with the HLA (human leukocyte antigen) marker system. One possible explanation for these associations is that two-locus inheritance may be involved in the genetics of the disease. Moreover, separate evidence suggests two-locus inheritance for two diseases in particular: IDDM and coeliac disease. In order to develop the full potential of linkage analysis, this proposal will attempt to solve three problems relating to disease-marker associations and two-locus inheritance: A. the effects of association on a linkage analysis; B. the problems of reduced penetrance due to a second genetic locus, for a linkage analysis; and C. genetic interpretation of the association (genetic modeling). In each case, the problem will be defined and quantified; then it will be solved by developing new methodologies. As each of the three problems in this project is addressed, the resulting solution will be applied to available data on four diseases well known to exhibit associations with the HLA marker system: insulin-dependent diabetes mellitus (IDDM), multiple scerosis, ankylosing spondylitis, and coeliac disease. Better understanding of the genetics of these diseases will lead eventually to better treatment or prevention.